The sundial is one of the earliest scientific instruments created by mankind. Thousands of years ago, almost every culture of the world independently discovered the principle of determine the day in a year and the time in a day by observing the position of the sun, and invented some type of the sundial. Although the mechanical clock was invented in the 16th century, until late 19th century, the sundial was still used as a reliable time piece in Europe. Even more recently, novel types of sundials are being invented. Most known sundials use a gnomon, which is an opaque piece of solid material that can project a shadow on a panel. The gnomon can be a long and thin opaque stylet or an opaque sphere. Because the sun has a finite radius, the shadow is typically fussy. Some sundials use a hole and or equivalently, a mirror to project a bright spot on the panel instead of a dark shadow. Because the angle of rotation of the sun often exceeds 180 degree, the hole can only be effective for a small range of angles, thus its usefulness is limited. To improve the sharpness of the image, some sundials use a concave mirror or a cylindrical mirror to focus the sun beam. However, the focus surface is a special curved surface in the three-dimensional space, which must be strictly arranged and followed. And, similar to the case of curved mirrors, if the sun beam is seriously off the axis, the sharpness of the image is low.
Another problem with the traditional sundials is that the angular position of the sun depends on the day of the year. The difference of the solar time and the average time is represented by the well-known equation of time. The error could be a large fraction of an hour. Therefore, the accuracy of the sundial is limited, especially the stylet and cylindrical-mirror type. Usually, a conversion table or conversion chart is attached to a sundial for the equation-of-time correction.
The magnetic compass is widely used for determining directions. However, the position of the magnetic North Pole is off about 10° from the true North Pole, and the magnetic South Pole is off about 25° from the true South Pole. In the United States, the error (magnetic inclination) could be as large as 20°. The magnetic inclination also varies year by year. Furthermore, the magnetic compass is greatly affected by the ferromagnetic materials in the neighborhood of a compass, e.g., iron ore in the ground or any steel or iron pieces.
In 1834, W. A. Burt invented the solar compass which uses the position of the sun to determine the true north. Because of its reliability and accuracy, since the middle of the 19th century, the US government defined the solar compass as the standard for land surveying. The solar compass is also used in the military for reliably determining the directions in the battle field. However, the operation of known solar compasses is complicated and requires the calculation of the local solar time versus the local standard time at the time of measurement, and requires elaborate manual adjustments. When a gnomon is used, the same inaccuracy problem with the sundials, the fussiness of the image and the equation of time, is present.
It is well known that a convex lens can focus sunlight into a sharp spot. However, it works only when the position of the sun is aligned with the axis of the lens. When the sun is slightly off the axis, the image is distorted. If the sun is seriously off the axis, the image is grossly distorted and eventually disappears. Furthermore, the depth of field is usually quite shallow. The use of convex lens in solar compass requires manual adjustment to align the axis with the sun.